An e-mail alert to neighbors groups in North Cambridge shows the Cambridge Crossing apartment project has another — possibly final — auction date set for 11 a.m. Tuesday. There have been five delays since the original Sept. 15, 2010, date, soon after which developer Joseph Perroncello declared bankruptcy.

The former St. John’s Religious Education Catholic school and convent at Yerxa Road and Rindge Avenue consists of three buildings, only one of which is finished and renting. An estimated $5 million is needed to complete it, according to court filings in the war for control of the site between Perroncello and Broder-Rindge Properties, which took on the mortgage as of May 9 when it was sold from under Perroncello by an impatient Webster Bank.

The war for control was lost by Perroncello on Aug. 8, when U.S. Bankruptcy Judge Frank Bailey dismissed his argument, based on a reading of legal language that seemed to contain a loophole, that Broder bought the 2.2-acre parcel with the same restrictions as the bank but not the same rights — meaning Broder had no right to run an auction, even though it bought the property from a bank that did.

Calling Perroncello the loser in that argument, the judge had other issues to address.

“As this case is now in its tenth month,” the judge said, Perroncello needs “a mature and detailed plan [for the site] and strong evidence that it is likely to come to fruition.”

But there was neither, Bailey noted:

“First, the properties are not necessary for a successful [bankruptcy] reorganization. The debtor has many other properties and can more feasibly fashion a plan that does not retain those that are subject to Broder-Rindge’s mortgage. … the completion of these properties would more likely be a drag on or detriment to his reorganization efforts than a boon.

“Second and more importantly, any plan that would retain the present properties would be contingent on the debtor’s obtaining some $5 million in financing to fund their completion. The debtor has articulated no strategy for obtaining this financing that does not involve a priming lien that would subordinate Broder-Rindge’s secured claim to the new financing, and the debtor has articulated no realistic basis on which the court could … approve such a priming lien.”

“The debtor simply has not dealt realistically with the adequate protection of Broder-Rindge’s secured claim,” Bailey said.

The auction may be a way for Broder itself to continue the project, which has the potential to hold 63 apartments. The company owns a 10-story building near Boston’s Post Office Square bought in 2007 for $19 million, and has developed condominiums in the South End’s Rutland Square.